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Trader Scott Gueli reacts on the floor of the New York Stock Exchange March 4, 2014. U.S. stocks rallied on Tuesday with the S&P 500 closing at a record high.Reuters

If you are trying to determine whether stocks are cheap or expensive after a five-year bull market, you are up against a formidable obstacle: confusion over earnings.

The S&P 500 has risen 183 per cent since 2009, making it one of the most impressive long-term rallies in recent history. But the rally is also leaving many observers wondering how long the good times can last.

The price-to-earnings ratio, using both trailing earnings and estimated earnings, provides some guidance. To most observers, the ratios suggest that stocks are fairly valued at present, leaving room for modest gains over the next year.

Unfortunately, there are many disagreements over where earnings are headed – providing plenty of fodder for bulls (stocks are reasonable) and bears (stocks are expensive), and headaches for anyone weighing their views.

At least everyone can agree upon the recent past: According to Bespoke Investment Group, first-quarter earnings for companies within the S&P 500 rose 6.2 per cent in the first quarter, year-over-year.

That's much better than the zero growth that analysts had been expecting and puts the index on track to produce earnings of $108.91 (U.S.) a share over the past 12 months. Based on the S&P 500's current level, the trailing P/E ratio is about 17.3.

This is where interpretation comes into play. Bespoke noted that the average P/E ratio going back to 1929 is just 15.35, making the current ratio nearly two percentage points higher than average. In other words, stocks are expensive.

But wait: If you think market history dating back 85 years is going back too far, then you can easily find a historical time frame to give you a more attractive valuation.

For example, going back 25 years, the average P/E ratio is 18.90, making stocks look cheap right now. Or, if you prefer something more recent, the P/E ratio over the past 10 years has averaged nearly 17 – making today's level look perfectly reasonable.

The situation gets more baffling when you start picking away at earnings expectations, which are key to any forward-looking measure of the stock market's valuation.

Dan Suzuki, equity strategist at Bank of America, expects the S&P 500 to generate earnings of $127 a share in 2015, up from an estimated $118 in 2014, based on rising business confidence and spending, along with modest U.S. and global economic growth.

That should be enough to keep the bull market going and drive the S&P 500 to new heights; Bank of America believes the index will end this year at 2000, up from 1,888.03 on Wednesday afternoon.

But the problem with estimated earnings is that they are little more than guesses at this point, based on current economic trajectories.

As Mr. Suzuki noted, a global recession would skewer his estimations, driving down earnings to $93 a share – and driving up the P/E ratio. Of course, that would destroy all arguments for why the S&P 500 looks reasonably valued.

Valuation looks even worse when you average earnings over the past 10 years to account for the ups and downs in a typical business cycle. The Nobel Prize-winning economist and Yale University professor Robert Shiller believes this approach – called the cyclically adjusted price-to-earnings ratio – can deliver a better look at valuation.

Unfortunately, it currently shows earnings of just $75 a share for the S&P 500 – or a sky-high P/E ratio of 25.

Even Mr. Shiller will caution that his approach can't be relied upon to determine the near-term direction of the stock market.

However, you should keep it in mind when you hear anyone argue that stocks are cheap. Valuation is in the eye of the beholder.